Support and Validity
This article is going to be the first step in delving inside arguments in a way we have not yet done. So far we have looked at recognising arguments and their parts as well as standardising them. Now we will start to actually evaluate the arguments. This consists of two areas; support and truth. This article deals with support, but support cannot be explained without a knowledge of truth, so I will cover that very briefly.
Truth is a property of statements. A statement is true if the world actually is how the statement claims it is. It does not make sense to call an argument true.
Support is not a property of statements, it is a relationship between statements. Support is what we use to infer conclusions from premises. A good argument has premises that support its conclusion.
It is important to see how these concepts are different from one another. When evaluating an argument, we are looking at two questions;
- Are the premises true?
- Do the premises give support to the conclusion? (irrespective of their truth)
This article is about the second of those questions. Please do not ever refer to arguments as true or false, the terms do not apply!
In order to judge if premises support a conclusion, we need to assume that all the premises are true. We do this because we can work out that arguments are poor without needing to even find out if the premises are true or not. It may be the case that someone is talking about a field of which you have no knowledge and you can still discard their arguments. When looking at an argument, ask yourself ‘Assuming these premises are true, how likely is it that the conclusion is also true?’ Similarly you may ask ‘Assuming these premises are true, how unlikely is it that the conclusion is false?’
Deductive validity is when premises of an argument give complete support to its conclusion. This is often just called validity. As we shall not call arguments true, we should also never call statements or premises valid or invalid. Only arguments can be valid and invalid. Another way to define deductive validity is to say that if an argument is deductively valid, it is impossible for the premises to be true and the conclusion false. It does not matter if the premises actually are true or not, only that if they were true then the conclusion would also be true.
Validity is so strong a concept that if we take a valid argument and say its premises are true but its conclusion is false, we are forming a contradiction. A contradiction is when you are both asserting and denying the same thing. Explicit contradictions are statements such as “I am alive and I am not alive” and implicit contradictions are statements such as “I was born in 1985 but I was not alive in the 20th century”.
Using this principle, we can create an easy test for validity. If we take an argument and assert the premises with the negation of the conclusion and come to a contradiction, then we have a valid argument.
For instance, let’s use the argument “I am in Australia therefore I am in the southern hemisphere”. Asserting the premise with the negation of the conclusion would give…
I am in Australia
Therefore,
I am not in the southern hemisphere
This is a contradiction. If a contradiction is implicit, you can make it explicit by defining key terms, for instance ‘Australia = a country in the southern hemisphere’. The appearance of the contradiction is all we need to know that the original argument is valid.
Sometimes, arguments are not deductively valid, but this does not mean we should not accept them. For non-valid arguments, there can be different degrees of support. This judgement is somewhat subjective and most often is not able to be quantified (unless it is zero support). We use the terms complete, strong, moderate, weak and nil to talk about levels of support, but sometimes we may not even be able to be this precise. Again, these judgements are based on the assumption that the premises are true, so even false premises can give support to conclusions.
An example…
‘Last time I watched one of Stef’s videos, he was bald. Therefore, Stef is going to be bald in the next video I watch.’
In this case, the premise does not absolutely guarantee the conclusion (it would not be impossible for him to be sporting a foot high brightly coloured mohawk for example) but we can say (unfortunately perhaps – I’d love to see the mohawk!) that the premise gives strong support to the conclusion.
Another example…
‘The last 3 times I bet on black on roulette, I lost. Therefore, the game is rigged!’
This premise gives very weak support to the conclusion, although if the same thing happened for 100 spins the degree of support would certainly increase. The degree of support here could never be complete though, as it is not logically impossible for a fair wheel to always come up red.
Overall, the more realistic the possibility is for premises to be true and their conclusion to be false, the weaker the support is. Use your judgement fairly when evaluating support, it can sometimes be tricky. Think about hypothetical cases to help you judge the probability.
We have seen that arguments can have varying degrees of support, from nil to complete, and it is important to note how special the case of complete support – or deductive validity – actually is. Deductive validity is the basis for mathematical proof as well as formal logic. My next article is going to take a small sidetrack to give you a brief idea of what formal logic is, including a little bit of history; how it started with Aristotle, and what it is like today.
It is important to recognise the shortcomings of formal logic though. In formal systems, support is considered to be either complete or not, there are no degrees of support. This less formal method that we have been talking about allows you to judge a wider range of arguments. For instance, the argument I gave earlier about Stef and the mohawk is invalid, but the degree of support is still strong. It is for these kinds of arguments that degrees of support is a useful concept, as formal logic is an all-or-nothing matter.